Vertex-Minimal Triangulation of Complexes with Homology
Kogan, Jon V. · arXiv (Cornell University) · 2025
For a given pair of numbers $(d,k)$, we establish the minimal number of vertices in pure $d$-dimensional simplicial complexes with non-trivial homology in dimension $k$. Furthermore, we solve the problem under the additional constraint of strong connectivity with respect to any intermediate dimension.